Young's Double Slit Experiment | Wave Optics | Class 12 Physics | NEET

When the entire YDSE apparatus is immersed in a medium of refractive index μ, the wavelength becomes λ' = λ/μ. The fringe width becomes β' = λ'D/d = (λ/μ)D/d = β/μ. Thus, the fringe width decreases when the apparatus is immersed in a denser medium. The angular fringe width becomes Δθ' = λ'/d = (λ/μ)/d = Δθ/μ.

In Young's Double Slit Experiment, placing a mica sheet with refractive index μ = 3/2 in front of one slit creates a path difference of (μ - 1)t. To reduce the intensity at the screen's center to half the maximum, the phase difference must be π/2, corresponding to a path difference of λ/4. Solving (μ - 1)t = λ/4 gives t = λ/[(μ - 1) × 4] = λ/[(1/2) × 4] = λ/2.

This section addresses the effect of immersing the entire Young's double slit apparatus in a liquid of refractive index μ. When light enters a medium, the frequency remains unchanged (determined by the source), but the velocity and wavelength change. The wavelength in the medium is: λ_medium = λ_air/μ. The fringe width in the medium becomes: β_medium = (λ_air/μ) × (d/D). The wavelength decreases by a factor of μ, so the fringe width also decreases by the same factor. A numerical example is provided: λ = 690 nm, d = 1.5 mm, D = 0.72 m, μ = 1.44, giving β = 0.23 mm.

When YDSE is immersed in a medium of refractive index μ, the wavelength becomes λ' = λ/μ. The angular fringe width becomes θ' = θ/μ. If the separation between coherent sources is halved (d' = d/2) and screen distance is doubled (D' = 2D), the fringe width becomes β' = 4β. The intensity at path difference Δx = λ is I = 4I₀. If this intensity is given as K, then I₀ = K/4.

When the entire Young's Double Slit Experiment (YDSE) apparatus is immersed in a liquid, the fringe width decreases because the wavelength of light in the liquid is less than in air, as the refractive index of the liquid is greater than 1, which reduces the wavelength according to the relationship λ = λ₀/n, where λ₀ is the wavelength in vacuum and n is the refractive index of the medium.

To determine whether an interference pattern is from single slit diffraction or double slit interference, observe the following: (1) In single slit diffraction, the central bright fringe is wider than secondary fringes, and brightness decreases progressively away from center. (2) In double slit interference, all fringes are equal in width, and brightness remains relatively uniform. The number of fringes alone does not indicate which type of pattern it is.

Single slit diffraction produces a different interference pattern compared to double slits. The single slit pattern has a very intense central maximum that is double the width of the secondary maxima. The central bright fringe is much brighter and wider than the other fringes. In contrast, double slit interference produces equally spaced bright fringes with gradually decreasing intensity. Both patterns involve diffraction, but the single slit pattern is dominated by the diffraction effect from a single aperture, while the double slit combines both diffraction and interference effects.

Diffraction is the bending of light around obstacles or through narrow openings. It produces alternating bright and dark regions similar to interference patterns. The central maximum is brightest, with intensity decreasing progressively outward. Single slit diffraction minima occur at a sinθ = nλ (n = ±1, ±2...). Secondary maxima occur approximately at a sinθ = (n + 1/2)λ. The pattern results from superposition of waves from different parts of the slit. The distinction between interference and diffraction is not absolute - Young's double slit pattern can be viewed as superposition of diffraction patterns from each slit.

When light passes through a narrow slit, it creates a diffraction pattern on a screen with alternating bright and dark fringes. Key characteristics distinguish this from interference: (1) The central bright fringe is the widest and brightest; (2) Subsequent bright fringes decrease in width and brightness progressively; (3) Dark fringes are equally spaced but not equally bright; (4) Fringe width decreases as you move away from the center. These features arise because each point on the slit acts as a secondary source according to Huygens' principle.

Single-slit diffraction is fundamentally the same phenomenon as interference but is distinguished by convention. When light passes through a single slit, each point in the aperture acts as a Huygens source, and the resulting interference creates a broad central maximum with alternating bright and dark regions. The distinction between 'diffraction' and 'interference' is largely historical and semantic—both describe wave superposition. The key difference is that single-slit diffraction involves a continuous distribution of sources rather than discrete ones.

Single-slit diffraction creates central maxima with secondary maxima of decreasing intensity. The first minimum occurs at a × sin(θ) = λ. Resolving power determines ability to distinguish close objects: d = 1.22λ/(NA) for microscopes and d = 1.22λ/D for telescopes. These principles explain optical instrument limitations and diffraction-limited imaging.

The resolving power of an optical instrument is its ability to distinguish between two closely spaced point objects, determined by the Rayleigh criterion where two objects are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other, given by the formula θ = 1.22λ/(a sinθ), where λ is the wavelength of light, a is the aperture size, and θ is the angle of observation; this principle applies to both microscopes and telescopes, with the resolving power being inversely proportional to the limit of resolution.

The limit of resolution is the minimum angular separation between two point sources that can be distinguished as separate entities. According to Rayleigh's criterion, two points are just resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other. The minimum angle θ_min = 1.22λ/D, where λ is the wavelength of light and D is the aperture diameter. Resolving power is inversely related to this limit. For telescopes, resolving power increases with larger aperture and decreases with longer wavelength. For microscopes, resolving power also depends on numerical aperture (NA = n sin β).

This segment covers resolving power and the diffraction limit of optical instruments. The instructor explains that the resolving power of an optical instrument is given by the formula R = 1/(θ_min), where θ_min is the minimum angular separation that can be resolved. For a circular aperture, θ_min = 1.22λ/D, where λ is the wavelength and D is the diameter of the aperture. The segment also covers the diffraction limit, explaining that all optical instruments are limited by diffraction, which prevents them from achieving infinite resolution. This limit is determined by the wavelength of light and the size of the aperture. The instructor emphasizes that these concepts are fundamental to understanding wave optics and are essential for students to grasp.

Polarization converts unpolarized light (oscillating in multiple planes) to polarized light (oscillating in one plane). Polaroids are special crystals that achieve this. When unpolarized light of intensity I₀ passes through a polarizer, intensity becomes I₀/2. An analyzer checks polarization. Malus's Law states that intensity after the analyzer is I = I₀cos²θ, where θ is the angle between polarization direction and analyzer axis. This demonstrates the transverse nature of light waves.

Polarization of light occurs when light waves oscillate in a single plane rather than in all directions perpendicular to propagation; when unpolarized light passes through a polarizer, only the component oscillating parallel to the polarizer's axis is transmitted, with intensity following Malus's law (I = I₀cos²θ). Brewster's angle (θb) is the angle of incidence at which reflected light becomes completely polarized, satisfying the condition tan(θb) = μ, where μ is the refractive index of the medium.

Polarization is a transverse wave property—longitudinal waves cannot exhibit it. Unpolarized light vibrates in all directions perpendicular to propagation. Passing through a polarizer restricts vibrations to one plane, producing polarized light with intensity halved. Malus' law describes polarized light passing through a second analyzer: I = I₀/2 × cos²(θ), where θ is the angle between polarizer and analyzer. At 90°, no light passes; at 0°, maximum intensity transmits. This demonstrates light's transverse nature. Two key definitions: plane of vibration contains the electric field vector, while plane of polarization is perpendicular to it. Methods of polarization include transmission through dichroic substances, reflection (Brewster's law), and scattering.

Polarization restricts light vibrations to one plane. Unpolarized light has electric field vectors vibrating in all directions perpendicular to propagation. When passing through a polarizer, only the component in a particular direction passes through. Malus's Law states transmitted intensity I = I0 cos²(θ), where θ is the angle between polarization direction and transmission axis. At θ = 90°, intensity becomes zero (crossed polarizers). This demonstrates the transverse nature of light and is used in various optical applications.

Polarization proves light is transverse. Brewster's Law states that at the polarizing angle, tan(i_p) = n, where n is the refractive index. At this angle, reflected light is completely polarized, and the reflected and refracted rays are perpendicular (90° angle between them). For air-to-glass with n = 4/3, i_p ≈ 53.1°.